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ChemistryEdu Logo Solution | Colligative Properties of Dilute Solution#

Colligative Properties#

  • Colligative properties are the properties which depend on the number of solute particles present in the solution irrespective of nature of solute.

Four colligative properties:#

  • Relative Lowering of vapour pressure (RLVP)
  • Elevation in boiling point
  • Depression in freezing point
  • Osmotic Pressure

1. Relative Lowering of vapour pressure#

  • When a non-volatile solute is added to a pure solvent, its vapour pressure decreases. This decrease in vapour pressure is known as lowering of vapour pressure.

Lowering of V.P = po - ps

where, po = V.P of pure solvent

and, ps = V.P of solution

  • Relative lowering of vapour pressure is defined as:
\[RLVP = {p_o - p_s\over p_o}\]
  • Since, ps = poΧsolvent, therefore, we can write:
\[RLVP = {p_o - p_oΧ_{solvent}\over p_o}\]
\[RLVP = {1 - Χ_{solvent}}\]
\[∴\ RLVP = Χ_{solute} \]
  • Hence, we can conclude that:
\[RLVP = {p_o - p_s\over p_o} = {Χ_{solute}}\]

Remember

Lowering of V.P is not a colligative property. Relative lowering of V.P is a colligative property.

2. Elevation of Boiling Point#

  • The boiling point of a solution is the temperature at which the vapour pressure of solution becomes equal to the atmospheric pressure or external pressure.

  • Boiling point depends on external pressure. As external pressure changes, boiling point will also change.

  • When a non-volatile solute is added to a solvent, then its boiling point will increase, ie, boiling point of a solution is always greater than pure solvent.

  • This increase in boiling point of pure solvent is known as elevation of boiling point. If Tb is the boiling point of solution and Tob is the boiling point of pure solvent, then elevation of boiling point, ΔTb is given by:

\[ΔT_b = T_b - T^o_b\]
  • Elevation of boiling point is directly proportional to molality of solute in the solution.
\[ΔT_b\ ∝\ m\]
\[ΔT_b = {K_b\ m}\]
\[where, K_b = {Molal\ elevation\ constant}\]

3. Depression of Freezing Point#

  • Freezing point is the temperature at which the vapour pressure of solid becomes equal to atmospheric pressure.

  • When a non-volatile solute is added to a pure solvent, its freezing point decreases. This decrease in freezing point is known as depression of freezing point.

  • If Tf is the freezing point of solution and Tof is the freezing point of pure solvent, then:

\[ΔT_f = {T^o_f - T_f}\]
  • Depression of freezing point is directly proportional to molality of solute dissolved in the solution.
\[ΔT_f\ ∝\ m\]
\[ΔT_f = {K_f\ m}\]
\[where, K_f = {Molal\ depression\ constant}\]

4. Osmotic Pressure#

  • Osmosis: The spontaneous flow of solvent molecules from a dilute solution to a concentrated solution through a semi-permeable membrane is called osmosis.

  • Osmotic Pressure: The pressure required to stop the movement of solvent molecules from a dilute solution to a concentrated solution through a semi-permeable membrane is called osmotic pressure. It is directly proportional to concentration of solution and is given by:

\[Π = {CRT}\]
\[where, Π = Osmotic\ Pressure\]
\[C = concentration\ of\ solution\]
\[R = Universal\ Gas\ Constant\]
\[T = Temperature\]

  • Reverse Osmosis(RO): If a pressure greater than osmotic pressure is applied, the direction of osmosis is reversed and the process is known as reverse osmosis. This principle is used by water filters.

  • Isotonic Solutions: Two solutions having same osmotic pressure are called isotonic solutions.

  • Hypertonic Solution: The solution having higher osmotic pressure as compared to other solution is known as hypertonic solution.

  • Hypotonic Solution: The solution having lower osmotic pressure as compared to other solution is known as hypotonic solution.

Remember

Hypertonic solution and hypotonic solution are relative terms. A solution X may be hypertonic as compared to another solution Y but may be hypotonic for solution Z.